Europium in plagioclase-hosted melt inclusions reveals mantle melting modulates oxygen fugacity

To gain insights into the composition and heterogeneity of Earth’s interior, the partial pressure of oxygen (oxygen fugacity, or fO2) in igneous rocks is characterized. A surprising observation is that relative to reference buffers, fO2s of mantle melts (mid-ocean ridge basalts, or MORBs) and their presumed mantle sources (abyssal peridotites) differ. Globally, MORBs have near-uniform fO2s, whereas abyssal peridotites vary by about three orders of magnitude, suggesting these intimately related geologic reservoirs are out of equilibrium. Here, we characterize fO2s of mantle melting increments represented by plagioclase-hosted melt inclusions, which were entrapped as basaltic melts migrated from their sources toward the seafloor. At temperatures and fO2s constrained by rare earth element distributions, a range of fO2s consistent with the abyssal peridotites is recovered. The fO2s are correlated with geochemical proxies for mantle melting, suggesting partial melting of Earth’s mantle decreases its fO2, and that the uniformity of MORB fO2s is a consequence of the melting process and plate tectonic cycling.


Figure S1
Eu partition coefficients predicted using Eqs.6 and 8-14 and the equilibrium constant () determined from experimental observations (Eq.15), and residuals to the fit Figure S2 Demonstration of the Eu-in-plagioclase-melt oxybarometer's ability to reproduce experimentally imposed fO2s Figure S3 Calculated Eu partition coefficients plotted as a function of fO2 for three experiments Figure S4 Temperatures inverted from measured plagioclase-melt REE distributions in experiments compared to experimental temperatures Figures S5-S7 Temperature inversion diagrams for measured plagioclase-melt REE distributions in natural samples Figure S8 Partition coefficients calculated using the measured REE concentrations Figure S9 Covariations of Fe 3+ /(Fe 2+ +Fe 3+ ), An#, and FMQ with temperatures determined using Putirka's plagioclase-liquid equilibria thermobarometer 1

Figures S10-S12
Histograms showing results of Monte Carlo simulations used to calculate fO2 uncertainty Figure S13 Demonstration of the Eu-in-plagioclase-melt oxybarometer's ability to recover fO2s in natural samples previously determined using XANESbased Fe speciation data Figure S14 Lack of compositional correlations with experimental fO2 determined by Eu-in plagioclase oxybarometry

Figure S15
Lack of correlation between fO2 and experimental homogenization time References  Colored symbols represent experiments conducted on terrestrial basaltic systems that were used to determine the equilibrium constant in the present study [2][3][4][5] .Gray dots in background show model extrapolation to experimental data from simple, evolved, and planetary-relevant systems excluded from the equilibrium constant determination [6][7][8][9][10][11][12] .Error bars are calculated using the uncertainty in the equilibrium constant  (Supplementary Figure S1b, see Methods for details on the more comprehensive approach used to calculate uncertainty for natural samples).The oxybarometer accurately recovers most experimentally imposed fO2s in the calibration and extrapolation datasets over geologically relevant fO2s.(IW) and fayalite-magnetite-quartz 14 (FMQ) buffers at the experimental temperature and atmospheric pressure.Note the steep slope of the   curve within ~±5 log units of the FMQ buffer, which helps mitigate error propagation associated with uncertainty in the measured Eu partition coefficient at those fO2s.Flattening of the   curve at high and low fO2s (where   approaches divalent and trivalent Eu partition coefficients, respectively) makes the Eu-inplagioclase-melt oxybarometer susceptible to an unreliable result at those conditions.

Fig S4.
Temperatures inverted from trace element partitioning experiments that exhibit linear REE partition coefficient distributions in temperature inversion space (e.g., Supplementary Fig. S5) (y axis) plotted against experimental temperature (x axis).Uncertainty shown by the error bars is determined from the slope of the line in the temperature inversions (see Supplementary Figs.S5-S7).With the exception of the data of Laubier et al. 4 (which reported 2-4 REE partition coefficients for each experiment, excluding Eu) and a few outliers from other studies 7,11 , the thermometer systematically recovers the experimental temperatures from the measured partitioning data.plotted against the log of the oxygen fugacity log(fO2) recovered using Eqs.7-15 (a), molar Fe 3+ /(Fe 2+ +Fe 3+ ) in glass calculated using the model of Kress and Carmichael 20 (b), plagioclase An# (100×Ca/(Ca+Na+K), in moles) (c), and relative to the fayalite-magnetite-quartz buffer (Δ FMQ) at 0.4 GPa 14 (d).Circles in the background of (c) are plagioclase-saturated experiments with oceanic basalt and basaltic andesite liquids (downloaded from the LEPR database 21 ).Despite the more limited range of temperatures recovered using Putirka's thermometer than Eqs.16-19, the variations of temperature with Fe 3+ /(Fe 2+ +Fe 3+ ) and Δ FMQ are qualitatively consistent with trends shown in Fig. 5 in the main text.Comparison of Fig. 5c and Supplementary Fig. S9c demonstrates that the REE equilibration temperature inversion method produces covariations of temperature and An# more consistent with experiments.

Fig. S10.
Histograms showing distributions of oxygen fugacities (fO2s) recovered using Eqs.7-19 for the samples investigated in this study using Monte Carlo simulations.Deviation from the fayalite-magnetite-quartz buffer (ΔFMQ) is calculated using the parameterization of Frost 14 .Reported fO2 uncertainty is the standard deviation of fO2s calculated from 1000 synthetically perturbed datasets of input parameters.The simulations incorporate the following sources of uncertainty: , , , major and trace element compositions, and lattice strain model coefficients (Eqs.6a-7c, Sun et al., 2017 5 ), see Methods for details.

Fig. S1 .
Fig. S1.Eu partition coefficients (DEu) predicted using the equilibrium constant () determined from application of Eqs. 6 and 8-14 to experimental observations from terrestrial basaltic systems 2-5 (Eq.15, see Methods).Predicted Eu partition coefficients are mostly within uncertainty of the calibrating observations (a); vertical error bars are estimated from the uncertainty in the equilibrium constant, horizontal error bars are reported in the literature.Residuals from the fit exhibit a normal distribution (b) from which the uncertainty in the equilibrium constant is determined.

Fig. S2 .
Fig. S2.Demonstration of the Eu-in-plagioclase-melt oxybarometer's ability to reproduce experimentally imposed oxygen fugacities (fO2s).Colored symbols represent experiments conducted on terrestrial basaltic systems that were used to determine the equilibrium constant in the present study[2][3][4][5] .Gray dots in background show model extrapolation to experimental data from simple, evolved, and planetary-relevant systems excluded from the equilibrium constant determination[6][7][8][9][10][11][12] .Error bars are calculated using the uncertainty in the equilibrium constant  (Supplementary FigureS1b, see Methods for details on the more comprehensive approach used to calculate uncertainty for natural samples).The oxybarometer accurately recovers most experimentally imposed fO2s in the calibration and extrapolation datasets over geologically relevant fO2s.See Supplementary Fig.S3for an explanation of the deviation of predicted from experimental fO2s for experiments conducted in air.

Fig. S3 .
Fig. S3.Calculated Eu partition coefficients (DEu) plotted as a function of oxygen fugacity (fO2) using Eqs.6 and 8-14 (solid blue curves) compared to measured Eu partition coefficients at the experimentally imposed fO2s (triangles).Panels (a), (b), and (c) each show an individual experimental result and the corresponding DEu prediction.Experimental conditions, the experiment name, and the data sources are provided in the panels.Dotted curves show DEu uncertainty propagated from the uncertainty in the equilibrium constant ().Error bars on the symbols are reported in the experimental literature.Black and magenta lines show the ironwüstite13 (IW) and fayalite-magnetite-quartz14 (FMQ) buffers at the experimental temperature and atmospheric pressure.Note the steep slope of the   curve within ~±5 log units of the FMQ buffer, which helps mitigate error propagation associated with uncertainty in the measured Eu partition coefficient at those fO2s.Flattening of the   curve at high and low fO2s (where   approaches divalent and trivalent Eu partition coefficients, respectively) makes the Eu-inplagioclase-melt oxybarometer susceptible to an unreliable result at those conditions.

Fig. S5 .
Fig. S5.Temperature inversions for samples investigated in this study and complied from the literature.Eu (flagged in light blue) falls off the trends defined by trivalent elements, and is excluded from the temperature determinations by a robust fitting algorithm.Uncertainty in the recovered temperatures is estimated using uncertainty in the slope of the best fit line.See Supplementary Data 3 for a summary of the input data and results.

Fig. S6 .
Fig. S6.Temperature inversions for samples investigated in this study and complied from the literature.Eu (flagged in light blue) falls off the trends defined by trivalent elements, and is excluded from the temperature determinations by a robust fitting algorithm.Uncertainty in the recovered temperatures is estimated using uncertainty in the slope of the best fit line.See Supplementary Data 3 for a summary of the input data and results.

Fig. S7 .
Fig. S7.Temperature inversions for samples investigated in this study and complied from the literature.Eu (flagged in light blue) falls off the trends defined by trivalent elements, and is excluded from the temperature determinations by a robust fitting algorithm.Uncertainty in the recovered temperatures is estimated using uncertainty in the slope of the best fit line.See Supplementary Data 3 for a summary of the input data and results.

Fig. S8 .
Fig. S8.Partition coefficients calculated using trace element data summarized in Supplementary Data 2 and 3.

Fig. S9 .
Fig. S9.Temperatures calculated using the plagioclase-liquid thermobarometer of Putirka 1 plotted against the log of the oxygen fugacity log(fO2) recovered using Eqs.7-15 (a), molar Fe 3+ /(Fe 2+ +Fe 3+ ) in glass calculated using the model of Kress and Carmichael 20 (b), plagioclase An# (100×Ca/(Ca+Na+K), in moles) (c), and relative to the fayalite-magnetite-quartz buffer (Δ FMQ) at 0.4 GPa 14 (d).Circles in the background of (c) are plagioclase-saturated experiments with oceanic basalt and basaltic andesite liquids (downloaded from the LEPR database21 ).Despite the more limited range of temperatures recovered using Putirka's thermometer than Eqs.16-19, the variations of temperature with Fe 3+ /(Fe 2+ +Fe 3+ ) and Δ FMQ are qualitatively consistent with trends shown in Fig.5in the main text.Comparison of Fig.5cand Supplementary Fig.S9cdemonstrates that the REE equilibration temperature inversion method produces covariations of temperature and An# more consistent with experiments.

Fig. S11 .
Fig. S11.Histograms showing distributions of oxygen fugacities (fO2s) recovered using Eqs.7-19 for the samples investigated in this study using Monte Carlo simulations.Deviation from the fayalite-magnetite-quartz buffer (ΔFMQ) is calculated using the parameterization of Frost14 .Reported fO2 uncertainty is the standard deviation of fO2s calculated from 1000 synthetically perturbed datasets of input parameters.The simulations incorporate the following sources of uncertainty: , , , major and trace element compositions, and lattice strain model coefficients (Eqs.6a-7c, Sun et al., 20175 ), see Methods for details.

Fig. S12 .
Fig. S12.Histograms showing distributions of oxygen fugacities (fO2s) recovered using Eqs.7-19 for the samples investigated in this study using Monte Carlo simulations.Deviation from the fayalite-magnetite-quartz buffer (ΔFMQ) is calculated using the parameterization of Frost14 .Reported fO2 uncertainty is the standard deviation of fO2s calculated from 1000 synthetically perturbed datasets of input parameters.The simulations incorporate the following sources of uncertainty: , , , major and trace element compositions, and lattice strain model coefficients (Eqs.6a-7c, Sun et al., 20175 ), see Methods for details.

Fig. S13 .
Fig. S13.A comparison of oxygen fugacities (fO2s) relative to the fayalite-magnetite-quartz buffer14 (Δ FMQ) at atmospheric pressure and 1200°C calculated using measured Eu distributions and major element compositions (Eqs.7-15, this study, y axis) and an Fe-speciation based method, X-ray absorption near edge spectroscopy (x axis, Cottrell and Kelley16 ).Uncertainties in the Eu-based method are propagated through the oxybarometer as described in the Methods, and as shown in Supplementary Fig.S11.The error bars in this figure are plotted as 2σ uncertainties, data in the main text are plotted with 1σ uncertainties.The comparison demonstrates that the Eu-in-plagioclase-melt method (Eqs.7-15) recovers fO2s consistent with XANES-based methods from natural samples.

Fig. S15 .
Fig. S15.Oxygen fugacities (fO2s) determined using measured plagioclase-melt inclusion glass Eu distributions relative to the fayalite-magnetite-quartz buffer22 (Δ FMQ) at atmospheric pressure plotted against experimental homogenization time (hours).Melt inclusion-bearing phenocrysts are heated to their estimated liquidus temperatures in air in a vertical tube furnace, then quenched (see the Methods for details).Note the fO2s are consistent with origination of the melt inclusions from relatively reduced sources, and do not exhibit systematic correlation of recovered fO2 with experimental time, consistent with them being unperturbed by the homogenization procedure.